A slit of width a is illuminated by monochromatic light of wavelength 650 mm at normal incidence calculate the value of a when
(a). The first minimum falls at an angle of diffraction of `30^(@)`
(b). The first maximum falls at an angle of diffraction of `30^(@)`.

Explanation

To solve the problem, we will use the conditions for minima and maxima in single-slit diffraction.

### Given:
- Wavelength of light, \( \lambda = 650 \, \text{nm} = 650 \times 10^{-9} \, \text{m} \)
- Angle of diffraction for both cases, \( \theta = 30^\circ \)

### (a) Finding the slit width \( a \) when the first minimum falls at \( 30^\circ \):

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